Singapore is 75% chinese, 15% malay and 10% Indian. Most malays and indians DO NOT speak chinese and are as successful as chinese. In fact many Chinese in singapore do not speak Chinese or speak better english than chinese. Furthermore the variety of dialect groups of Chinese in Singapore is so large that learning mandarin will not necessarily help you communicate with the older population. Its better to know a bit of every one of the languages than know only one very wellto get by. If you're thinking of singlish while words like "kena" come from chinese dialects (not mandarin), others such as "alamak" come from other languages such as malay.

As someone who has lived here for three years and travels around a lot in Singapore, not speaking mandarin can be problematic, particularly at some of the hawkers - but in precisely the same way not speaking Spanish was problematic in redwood city California (near Palo Alto).

Honestly, not being able to understand/speak singlish is probably a larger barrier to fitting in than not speaking mandarin.